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generally delocalized because of mode-mode coupling
effects or Fermi resonances between vibrational modes
and overtones. Therefore, a vibrational normal mode
cannot be exclusively assigned to an individual bond or a
particular structural unit. A solution to this problem will
be presented in the next section.
Results and Discussions
Cremer and co-workers have recently demonstrated
that for each molecule both a set of normal vibrational
modes and a unique set of local vibrational modes
exists. 4 The force constants of the local bond stretching
modes reliably describe the strength of the bonds of a
molecule. 5 Hence they can be used to investigate one of
the paradigm of chemistry which predicts that the shorter
bond of a given type is always the stronger bond. This has
been found to be fulfi lled in many cases on qualitative
grounds, 6 however there exists no theoretical proof of the
paradigm, which has to do with the elusiveness of the
chemical bond and the resulting diffi culty of defi ning the
bond strength.
In the following, we will demonstrate that it is
not generally true that the shorter bond is the stronger
bond. For this purpose, we consider the strength of the
NF bond in the series NH 2 F (1), NHF 2 (2), and NF 3
(3). Since these molecules are closely related, one can
assume that, according to the above paradigm, the NF
bond becomes stronger with decreasing NF bond length.
However, as shown in Figure 1, the calculated local
mode NF stretching force constants suggest the opposite:
the shorter NF bonds are the weaker. They also suggest
that the NH bonds behave normal in the series NH 3 (4),
1, 2 (Figure 1). Since these results are obtained with very
reliable quantum chemical methods (CCSD(T) 7 /cc-augpVTZ
8 for both geometry and local mode frequencies,
COLOGNE12 quantum chemistry package 9 ), there is
no doubt about the reliability of the results. Hence, they
have to be rationalized in the following.
The bond length can be considered as being close
to the sum of covalent radii of the atoms connected by
the bond. The covalent radius decreases with increasing
oxidation state of an atom, which is easy to determine
for transition metal cations but more diffi cult for the
atoms of the second period. In the series 1-3, the strong
withdrawal of negative charge by fi rst one, then two, and
fi nally three F atoms leads an increase of the positive
charge at the N atom (1: -288 me; 2: +186 me; 3: +636
me, see Figure 1) by almost 1 charge unit, which converts
the N atom effectively into a N cation with a smaller
covalent radius. Hence, the shorter bond length is just
a result of the different electron structure of the N atom,
which has lost almost 1e. The bond shortening in turn
causes an increase in pair repulsion between the electron
lone pairs at the F and the N atom. Despite the bond
shortening, destabilizing 4-electron interactions reduce
the bond strength. The NF local mode force constants
decrease with decreasing NF bond length and refl ect the
weakening of the NF bonds (Figure 1). Similar effects
can be always expected when strongly electronegative
substituents effectively reduce the covalent radius of a
central atom and this effect is accompanied by increasing
bond destabilization.
Figure 1. Local mode stretching force constants of NF and NH bonds
in NH 2 F (1), NHF 2 (2), NF 3 (3), and NH 3 (4) in dependence of the
equilibrium bond lengths R(NF) and R(NH) calculated at the CCSD(T)/
aug-cc-pVTZ level of theory. 7,8 (NF: bold line; NH: dashed line). NBO 12
charges are given in me.
In the case of the NH bonds, there is no lone pair
repulsion between the N and H atoms. Therefore, the
N-H bonds of 4 compared with those of 1 and 2 follow
the paradigm that shorter bonds are stronger bonds
(see Figure 1).
Another electronic effect, which can lead to an
inversion of the commonly expected bond length-bond
strength relationship is the relativistic mass-velocity
Jan / Jun de 2012 Revista Processos Químicos 33